If it's really the freewheel - and I don't recall ever seeing a freewheel that bad - You can tell if the freewheel is wobbly by just spinning the wheel withoiut pedaling. The freewheel will wobble back and forth. As the previous poster said that is not unusual (at least to a small degree) especially on less expensive bikes. Very inexpensive three piece hubs have been known fo fail enough so the flange is misaligned. I have even seen a few break loose completely. There is indeed nothing that will correct freewheel wobble other than a different hub. A cross threaded freewheel is possible but it takes a huge effort to tighten a cross threaded freewheel all the way down.

The problem is more likely to be derailleur adjustment, though - especially if it is an indexed system. The adjustment will be wrong for every gear if wrong for one. The other possibility is that the freewheel is not the proper one for the lever's indexing system.

I have never seen a wheel misalignment cause the behavior you describe (we're talking 1000's of bikes) and a very bad chainline would cause a problem on the chainwheel, not the freewheel.